How Does Timing Affect Annuity Calculations?

In summary, the final value of the plan in which payments of $800 are made every 6 months for 3 years, earning 10% interest compounded semi-annually, is $5,441.53. The first payment is made in 6 months.
  • #1
Imperil
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Find the final value of a plan in which payments of $800 are made every 6 months for 3 years, earning 10% interest compounded semi-annually. The first payment is made in 6 months.

My Answer:

R = 800, n = 6 , i = 5%

A = R[(1-i)^n - 1] / i

A = 800(1.05^6 - 1) / 0.05

A = $5441.53

So I calculated the annuity but I am thrown off by the last sentence. Since the first payment is made in 6 months does this mean that n should really be 5 because he is missing the first 6 months of the year? Or is 6 correct since it is semi-annual for 3 years? I'm just a little tripped up on the wording and started thinking that I am incorrect assuming n = 6 due to the final sentence.

Thanks
 
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  • #2
I would say n=6, because he is payed in 6 months time and then again in 6 months after that i.e. twice in the current year. This continues for another two years, for a total of 6 payments.
 
  • #3
Great thanks so much. That is what I originally thought but then started to second guess myself.
 

Related to How Does Timing Affect Annuity Calculations?

1. What is a sum/annuity?

An annuity is a financial product that involves a series of payments made at regular intervals over a specified period of time. The sum refers to the total amount of money that is invested in the annuity.

2. How does a sum/annuity work?

A sum/annuity works by an individual or entity making a lump sum payment to an insurance company or financial institution, which then invests the money and pays out a series of payments over time, either for a set period or for the rest of the individual's life.

3. What are the different types of annuities?

The three main types of annuities are fixed, variable, and indexed. Fixed annuities guarantee a set rate of return, while variable annuities allow for investment in various funds and have the potential for higher returns. Indexed annuities link the return to a specific market index.

4. What are the benefits of having a sum/annuity?

One benefit of having a sum/annuity is the ability to receive a steady stream of income over a period of time, which can provide financial stability and security. Annuities can also offer tax-deferred growth, meaning taxes are not paid on the earnings until the money is withdrawn.

5. What are the potential drawbacks of a sum/annuity?

One potential drawback of a sum/annuity is that there may be fees and penalties for early withdrawal, so it is important to consider the length of time the annuity will be held. Annuities may also have lower returns compared to other investment options and may not keep up with inflation.

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